Surface Area of Rectangular Prism: Express in Terms of X (3×5×X)

Express the surface area of the rectangular prism in terms of X using the given data.

Video Solution

Solution Steps

00:00 Express the surface area of the box

00:06 We'll use the formula for calculating rectangle area (side times side)

00:13 Calculate the area of each face

00:40 Since the box has 6 faces (2 of each type)

00:44 To calculate the surface area, multiply each area by 2 and sum

01:15 Group the terms

01:19 And this is the solution to the question

Step-by-Step Solution

To find the surface area of the rectangular prism in terms of $X$ , follow these steps:

Step 1: Identify the dimensions:
- Length $l = X$
- Width $w = 5$
- Height $h = 3$
Step 2: Use the surface area formula for a rectangular prism: $S = 2(lw + lh + wh)$
Step 3: Substitute the given values: $S = 2(X \cdot 5 + X \cdot 3 + 5 \cdot 3)$
Step 4: Simplify the expression: $S = 2(5X + 3X + 15)$ $S = 2(8X + 15)$ $S = 16X + 30$
Step 5: Therefore, the surface area of the rectangular prism expressed in terms of $X$ is $16X + 30$ .

This matches with choice 1.

Thus, the solution to the problem is $16X + 30$ .